Answer:
It will take 4.5hrs to cover the same distance
The constant of variation,k=252
Step by step explanation
Given that,
[tex]speed = \frac{distance}{time} [/tex]
From the question
Time=4hr
Speed=63km
By substitution we obtain,
[tex]63= \frac{distance}{4} [/tex]
Cross multiplying we get,
[tex]distance=63 \times 4[/tex]
[tex]distance=252km[/tex]
Now,
speed=56km
Distance Covered=252km
By substitution:
We obtain,
[tex]56= \frac{252}{time} [/tex]
Cross multiply
[tex]56\times time=252 [/tex]
Divide through by 56
[tex]time= \frac{252}{56} [/tex]
[tex]time=4.5hrs[/tex]
From the formula,
[tex]speed= \frac{distance}{time} [/tex]
Which means that, speed and time varies inversely.
[tex]speed\propto \frac{1}{time} [/tex]
Let k be variation constant
This implies that
[tex]speed = k \times \frac{1}{time} [/tex]
[tex]k=speed \times{time} [/tex]
Taken,
Time=4hrs
speed=56km
[tex]k=56\times4[/tex]
[tex]k=252[/tex]
